Penrose states that quantum effects can occur even in relatively large systems when energy differences remain small. This is just the situation with polymer materials. A quantum description by Penrose of the formation of quasi-crystals can be rewritten to apply to polymer crystallization. The implications of the need to take account of quantum effects are discussed. Another approach based on the quantization of energy levels in clusters of atoms offers a possible explanation of heat setting in nylon and polyester fibers. Finally some problems of the interpretation of quantum theory are discussed.